The correct option is A 9896.25 (102 × 98) (9.5 × 10.5)=(100 + 2) (100 2) [(10 0.5) (10 + 0.5)] =(100^2 2^2) (10^2 0.5^2) =10000 4 (100 0 ...

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Expanded Form of a Number

102× 98-9.5× ...

Question

$(102 \times 98) - (9.5 \times 10.5) =$

9896.25

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10095.75

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9897.75

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Solution

The correct option is A 9896.25
$(102 \times 98) - (9.5 \times 10.5) = (100 + 2) (100 - 2) - [(10 - 0.5) (10 + 0.5)]$
$= (100^{2} - 2^{2}) - (10^{2} - {0.5}^{2})$
$= 10000 - 4 - (100 - 0.25)$
$= 10000 - 104 + 0.25$
$= 9896 + 0.25 = 9896.25$

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Similar questions

Evaluate these using identity:

(i) 55 × 45; (ii) 33 × 27; (iii) 8.5 × 9.5; (iv) 102 × 98.

10.5

9.5

Using identities, evaluate:
$10.5 \times 9.5$ .

98 \times 10^{2}

98 $\times$ 102 = _____________.

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